Yes, but what does that mean? He was going to triumph militarily anyway. This would have presumably included a massacre and enslavement of all hostile populations. What could they have done against him anyway. How could it have been more complete?

I suspect that without the One there was a much higher possibility of resistance being maintained despite his victory, even as desperate and isolated pockets. With the One in his possession he would, presumably, be able to eradicate all opposition, however slight, and maintain this state of affairs for a much longer period of time.

For instance I imagine that his already vast empire, were the West added to it, would have been extremely unwieldy to control without the One allowing him to dominate the wills of his subjects. This may have particularly been a problem in the West as many of the older realms knew of him and his evil, which might have made their subjugation much more difficult than the wide lands to the East and South which had been blinded by the Shadow since the Elder Days.

Lacking the One would have also made it much more difficult for him to attack Rivendell and Lórien, perhaps impossible without coming himself, which would have possibly been a risk he was reluctant to take.

Overall I think it's a question of the pervasiveness and stability of his control with and without the One in his possession.

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"Since the evening of that day we have journeyed from the shadow of Tol Brandir."
"On foot?" cried Éomer.